Timelike entanglement entropy in dS$_3$/CFT$_2$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914632694759424 |
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| author | Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang |
| author_facet | Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang |
| contents | In the context of dS$_3$/CFT$_2$, we propose a timelike entanglement entropy defined by the renormalization group flow. This timelike entanglement entropy is calculated in CFT by using the Callan-Symanzik equation. We find an exact match between this entanglement entropy and the length of a timelike geodesic connecting two different spacelike surfaces in dS$_3$.The counterpart of this entanglement entropy in AdS$_3$ is a spacelike one, also induced by RG flow and extends all the way into the bulk of AdS$_3$. As a result, in both AdS$_3$/CFT$_2$ and dS$_3$/CFT$_2$, there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10376 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Timelike entanglement entropy in dS$_3$/CFT$_2$ Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang High Energy Physics - Theory In the context of dS$_3$/CFT$_2$, we propose a timelike entanglement entropy defined by the renormalization group flow. This timelike entanglement entropy is calculated in CFT by using the Callan-Symanzik equation. We find an exact match between this entanglement entropy and the length of a timelike geodesic connecting two different spacelike surfaces in dS$_3$.The counterpart of this entanglement entropy in AdS$_3$ is a spacelike one, also induced by RG flow and extends all the way into the bulk of AdS$_3$. As a result, in both AdS$_3$/CFT$_2$ and dS$_3$/CFT$_2$, there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry. |
| title | Timelike entanglement entropy in dS$_3$/CFT$_2$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2304.10376 |